



 
Hi Kelly, The quadratic expression x^{2}  2x + 15 can be factored to give x^{2}  2x  15 = (x  5)(x + 3). Thus the quadratic equation x^{2}  2x + 15 = 0 has roots x = 5 and x = 3. You can perform this from the end to the beginning. One quadratic equation with roots 5 and 3 is (x  5)(x + 3) = 0. Expanding this gives x^{2}  2x + 15 = 0. What I am saying is a quadratic equation with roots a and b is (x  a)(x  b) = 0. This fact is true, even if a and b are complex numbers. Hence one quadratic equation with roots 4  i and 4 + i is
Expand the left side. When you are finished you can use the quadratic formula to verify that 4  i and 4 + 1i are roots. Harley
 


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